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Students : Chemistry/Biology, Operations on rational nos.

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by anirudhbhalotia » Thu Mar 10, 2011 9:29 am
Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If atleast 30 of the students are not majoring in either Chemistry or Biology, then the no. of students majoring in both chemistry and biology could be any number from

A. 20 to 50
B. 40 to 70
C. 50 to 130
D. 110 to 130
E. 110 to 150

OA - D
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by srcc25anu » Thu Mar 10, 2011 11:35 am
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by VivianKerr » Thu Mar 10, 2011 12:03 pm
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The question asks what "x" could be.

150 = B + X

130 = C + X

B + C + X = 170

The MAXIMUM overlap is 130, since the Chemistry circle cannot be GREATER than 130. From there we know the answer must be either (C) or (D).

Plugging in our first two equations:

(150 - X) + (130 - X) + X = 170

150 - X + 130 - X + X = 170

150 - X + 130 = 170

150 - X = 40

- X = 40 - 150

-X = -110

X = 110

The answer is (D).
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